Yes it is compatible. This is totally fine, because the Arduino is open source.

Also, there are clones of the Arduino Uno that call themselves "Arduino Uno," and this is not fine, because Arduino is a registered trademark.

If you plan to make use of the Arduino support forums and tutorials, you might want to do your fair share in supporting those resources by buying a proper Arduino-branded device, though. Else you'd be a "moocher" -- using the support resources, but not using their boards. The clones are typically there for those who already know what they're doing, and just need more boards for cheap, but don't want to roll their own (which is another time-honored way of making cheap Arduinos.)